Finite Group Databasebeta

← Group #10710941

Character table — Group #10710941

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size112222222222222222244444444444444444448888888888888888888888888888888888242424242424242448484848
order122223444468812122424242422446668881212122424242424246688121216161616161616162424242448484848484848484848484848484848222244444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ61111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ71111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ81111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ9111-1-111-11-11-1-111-1-1-1-11-11-11-1-111-11-1-11111-1-11-11-11-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1-1111-1-1-1i−ii−i
χ10111-1-111-11-11-1-111-1-1-1-11-11-11-1-111-11-1-11111-1-11-11-11-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-1-1111−ii−ii
χ11111-1-111-11-11-1-111-1-1-1-11-11-11-1-111-11-1-11111-1-11-11-11-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii1-1111-1-1-1−ii−ii
χ12111-1-111-11-11-1-111-1-1-1-11-11-11-1-111-11-1-11111-1-11-11-11-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-1-1111i−ii−i
χ13111-1-111-11-11-1-111-1-1-1-1-11-111-1-111-11-1-11111-1-1-11-11-11ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-1-11-111i−i−ii
χ14111-1-111-11-11-1-111-1-1-1-1-11-111-1-111-11-1-11111-1-1-11-11-11ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii-1111-11-1-1−iii−i
χ15111-1-111-11-11-1-111-1-1-1-1-11-111-1-111-11-1-11111-1-1-11-11-11−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-11-111−iii−i
χ16111-1-111-11-11-1-111-1-1-1-1-11-111-1-111-11-1-11111-1-1-11-11-11−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i-1111-11-1-1i−i−ii
χ1722222222222-2-222-2-2-2-22222222-2-2-2222-2-2-2-2-2-222-2-22200000000-2-2-2-20000000000000000000000000000
χ1822222222222-2-222-2-2-2-2-2-2-2-2222-2-2-2222-2-2-2-2-2-2-2-222-2-20000000022220000000000000000000000000000
χ1922222-12222-122-1-1-1-1-1-12222-1-1-1222-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2022222-12222-122-1-1-1-1-1-12222-1-1-1222-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111000000000000
χ2122222-12222-122-1-1-1-1-1-1-2-2-2-2-1-1-1222-1-1-1-1-1-1-1-1-111-2-2112222-2-2-2-21111-1-1-1-1-1-1-1-111111111000000000000
χ2222222-12222-122-1-1-1-1-1-1-2-2-2-2-1-1-1222-1-1-1-1-1-1-1-1-111-2-211-2-2-2-22222111111111111-1-1-1-1-1-1-1-1000000000000
χ2322222-12222-1-2-2-1-111112222-1-1-1-2-2-2-1-1-1111111-1-1-2-2-1-100000000111133−3−333−3−333−3−333−3−3000000000000
χ2422222-12222-1-2-2-1-111112222-1-1-1-2-2-2-1-1-1111111-1-1-2-2-1-1000000001111−3−333−3−333−3−333−3−333000000000000
χ2522222-12222-1-2-2-1-11111-2-2-2-2-1-1-1-2-2-2-1-1-111111111221100000000-1-1-1-133−3−333−3−3−3−333−3−333000000000000
χ2622222-12222-1-2-2-1-11111-2-2-2-2-1-1-1-2-2-2-1-1-111111111221100000000-1-1-1-1−3−333−3−33333−3−333−3−3000000000000
χ27222-2-222-22-22222222222-22-22-2-2-2-222-2-2-2-2-2-2222-2-222-200000000-2-2220000000000000000000000000000
χ28222-2-222-22-2222222222-22-222-2-2-2-222-2-2-2-2-2-222-222-2-220000000022-2-20000000000000000000000000000
χ29222-2-2-12-22-2-122-1-1-1-1-1-12-22-2-111-2-22-1111111-1-1-11-22-110000000011-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3000000000000
χ30222-2-2-12-22-2-122-1-1-1-1-1-12-22-2-111-2-22-1111111-1-1-11-22-110000000011-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3000000000000
χ31222-2-2-12-22-2-122-1-1-1-1-1-1-22-22-111-2-22-1111111-1-11-12-21-100000000-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000
χ32222-2-2-12-22-2-122-1-1-1-1-1-1-22-22-111-2-22-1111111-1-11-12-21-100000000-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000
χ33222-2-2-12-22-2-1-2-2-1-111112-22-2-11122-2-111-1-1-1-111-112-2-112i2i−2i−2i2i2i−2i−2i-1-111−i−i−i−iiiii−i−i−i−iiiii000000000000
χ34222-2-2-12-22-2-1-2-2-1-111112-22-2-11122-2-111-1-1-1-111-112-2-11−2i−2i2i2i−2i−2i2i2i-1-111iiii−i−i−i−iiiii−i−i−i−i000000000000
χ35222-2-2-12-22-2-1-2-2-1-11111-22-22-11122-2-111-1-1-1-1111-1-221-12i2i−2i−2i−2i−2i2i2i11-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ36222-2-2-12-22-2-1-2-2-1-11111-22-22-11122-2-111-1-1-1-1111-1-221-1−2i−2i2i2i2i2i−2i−2i11-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000
χ3722-22-2222-2-2200-2-200002-2-22-22-200022-20000002-200-22−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3822-22-2222-2-2200-2-200002-2-22-22-200022-20000002-200-22i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3922-22-2222-2-2200-2-20000-222-2-22-200022-2000000-22002-2−i2i2−i2i2i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ4022-22-2222-2-2200-2-20000-222-2-22-200022-2000000-22002-2i2−i2i2−i2−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ4122-22-22-2-2222222222220000-22-22-2-2-2-2222-2-2-2-20000000000000000000000000000000000002-2002-20000
χ4222-22-22-2-2222222222220000-22-22-2-2-2-2222-2-2-2-2000000000000000000000000000000000000-2200-220000
χ4322-22-22-2-2222-2-222-2-2-2-20000-22-2-222-2-22-2-2222200000000000000000000000000000000002200-2-2000000
χ4422-22-22-2-2222-2-222-2-2-2-20000-22-2-222-2-22-2-222220000000000000000000000000000000000-2-20022000000
χ4522-22-2-122-2-2-1001133−3−32-2-221-11000-1-113−33−33−3-11001-1−i2i2−i2i2−i2i2−i2i23−33−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ4622-22-2-122-2-2-1001133−3−32-2-221-11000-1-113−33−33−3-11001-1i2−i2i2−i2i2−i2i2−i23−33−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ4722-22-2-122-2-2-1001133−3−3-222-21-11000-1-113−33−33−31-100-11−i2i2−i2i2i2−i2i2−i2−33−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ4822-22-2-122-2-2-1001133−3−3-222-21-11000-1-113−33−33−31-100-11i2−i2i2−i2−i2i2−i2i2−33−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ4922-22-2-122-2-2-10011−3−3332-2-221-11000-1-11−33−33−33-11001-1−i2i2−i2i2−i2i2−i2i2−33−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ5022-22-2-122-2-2-10011−3−3332-2-221-11000-1-11−33−33−33-11001-1i2−i2i2−i2i2−i2i2−i2−33−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ5122-22-2-122-2-2-10011−3−333-222-21-11000-1-11−33−33−331-100-11−i2i2−i2i2i2−i2i2−i23−33−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ5222-22-2-122-2-2-10011−3−333-222-21-11000-1-11−33−33−331-100-11i2−i2i2−i2−i2i2−i2i23−33−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ5322-2-2222-2-22200-2-2000022-2-2-2-220002-220000002200-2-22−2−222−2−2200002−22−2−22−222−22−2−22−22000000000000
χ5422-2-2222-2-22200-2-2000022-2-2-2-220002-220000002200-2-2−222−2−222−20000−22−222−22−2−22−222−22−2000000000000
χ5522-2-2222-2-22200-2-20000-2-222-2-220002-22000000-2-200222−2−22−222−200002−22−2−22−22−22−222−22−2000000000000
χ5622-2-2222-2-22200-2-20000-2-222-2-220002-22000000-2-20022−222−22−2−220000−22−222−22−22−22−2−22−22000000000000
χ5722-2-222-222-22222222220000-2-22-22-2-22-2-2-222-2-200000000000000000000000000000000002-200-22000000
χ5822-2-222-222-22222222220000-2-22-22-2-22-2-2-222-2-20000000000000000000000000000000000-22002-2000000
χ5922-2-222-222-22-2-222-2-2-2-20000-2-222-22-22-222-2-2220000000000000000000000000000000000002-200-220000
χ6022-2-222-222-22-2-222-2-2-2-20000-2-222-22-22-222-2-222000000000000000000000000000000000000-22002-20000
χ6122-2-22-12-2-22-1001133−3−322-2-211-1000-11-1−33−333−3-1-100112−2−222−2−22−333−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ6222-2-22-12-2-22-1001133−3−322-2-211-1000-11-1−33−333−3-1-10011−222−2−222−2−333−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ6322-2-22-12-2-22-1001133−3−3-2-22211-1000-11-1−33−333−31100-1-12−2−22−222−23−3−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ6422-2-22-12-2-22-1001133−3−3-2-22211-1000-11-1−33−333−31100-1-1−222−22−2−223−3−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ6522-2-22-12-2-22-10011−3−33322-2-211-1000-11-13−33−3−33-1-100112−2−222−2−223−3−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ6622-2-22-12-2-22-10011−3−33322-2-211-1000-11-13−33−3−33-1-10011−222−2−222−23−3−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ6722-2-22-12-2-22-10011−3−333-2-22211-1000-11-13−33−3−331100-1-12−2−22−222−2−333−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ6822-2-22-12-2-22-10011−3−333-2-22211-1000-11-13−33−3−331100-1-1−222−22−2−22−333−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ69444444-4-4-4-4400-4-400000000444000-4-4-40000000000000000000000000000000000000000000000000000
χ7044444-2-4-4-4-4-200222323−23−230000-2-2-200022223−23−2323−23230000000000000000000000000000000000000000000000
χ7144444-2-4-4-4-4-20022−23−2323230000-2-2-2000222−232323−2323−230000000000000000000000000000000000000000000000
χ72444-4-44-44-44400-4-4000000004-4-4000-4440000000000000000000000000000000000000000000000000000
χ73444-4-4-2-44-44-200222323−23−230000-2220002-2-2−232323−23−23230000000000000000000000000000000000000000000000
χ74444-4-4-2-44-44-20022−23−2323230000-2220002-2-223−23−232323−230000000000000000000000000000000000000000000000
χ7544-44-4-2-4-444-244-2-2-2-2-2-200002-224-4-422-2-2-222220000000000000000000000000000000000000000000000
χ7644-44-4-2-4-444-2-4-4-2-2222200002-22-44422-222-2-2-2-20000000000000000000000000000000000000000000000
χ7744-4-44-2-444-4-244-2-2-2-2-2-2000022-2-44-42-2222-2-2220000000000000000000000000000000000000000000000
χ7844-4-44-2-444-4-2-4-4-2-22222000022-24-442-22-2-222-2-20000000000000000000000000000000000000000000000
χ798-800080000-8−4i24i200−4i24i2−4i24i200000000000000000000000000000000000000000000000000000000000000000
χ808-800080000-84i2−4i2004i2−4i24i2−4i200000000000000000000000000000000000000000000000000000000000000000
χ818-8000-400004−4i24i243−434ζ5+4ζ7−4ζ5−4ζ74ζ13+4ζ23−4ζ13−4ζ2300000000000000000000000000000000000000000000000000000000000000000
χ828-8000-400004−4i24i2−43434ζ13+4ζ23−4ζ13−4ζ234ζ5+4ζ7−4ζ5−4ζ700000000000000000000000000000000000000000000000000000000000000000
χ838-8000-4000044i2−4i243−43−4ζ5−4ζ74ζ5+4ζ7−4ζ13−4ζ234ζ13+4ζ2300000000000000000000000000000000000000000000000000000000000000000
χ848-8000-4000044i2−4i2−4343−4ζ13−4ζ234ζ13+4ζ23−4ζ5−4ζ74ζ5+4ζ700000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.